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Simplifying (2x + 3)(x + 2) = 91 Reorder the terms: (3 + 2x)(x + 2) = 91 Reorder the terms: (3 + 2x)(2 + x) = 91 Multiply (3 + 2x) * (2 + x) (3(2 + x) + 2x * (2 + x)) = 91 ((2 * 3 + x * 3) + 2x * (2 + x)) = 91 ((6 + 3x) + 2x * (2 + x)) = 91 (6 + 3x + (2 * 2x + x * 2x)) = 91 (6 + 3x + (4x + 2x2)) = 91 Combine like terms: 3x + 4x = 7x (6 + 7x + 2x2) = 91 Solving 6 + 7x + 2x2 = 91 Solving for variable 'x'. Reorder the terms: 6 + -91 + 7x + 2x2 = 91 + -91 Combine like terms: 6 + -91 = -85 -85 + 7x + 2x2 = 91 + -91 Combine like terms: 91 + -91 = 0 -85 + 7x + 2x2 = 0 Factor a trinomial. (-17 + -2x)(5 + -1x) = 0Subproblem 1
Set the factor '(-17 + -2x)' equal to zero and attempt to solve: Simplifying -17 + -2x = 0 Solving -17 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -2x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2x = 0 + 17 -2x = 0 + 17 Combine like terms: 0 + 17 = 17 -2x = 17 Divide each side by '-2'. x = -8.5 Simplifying x = -8.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-8.5, 5}
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